John Harlim is a Professor of Mathematics and Meteorology at the Pennsylvania State University. His research interests include data assimilation and stochastic computational methods. In 2012, he received the Frontiers in Computational Physics award from the Journal of Computational Physics for his research contributions on computational methods for modeling Earth systems. He has previously co-authored another book, Filtering Complex Turbulent Systems (Cambridge, 2012).

'The MATLAB code used for the examples in the book can be downloaded from the publisher's website; the scripts are short, well commented and can be understood without difficulty (even if you are not a MATLAB expert).' Fabio Mainardi, MAA Reviews

• 1. Introduction; 2. Markov chain Monte Carlo; 3. Ensemble Kalman filters; 4. Stochastic spectral methods; 5. Karhunen–Loève expansion; 6. Diffusion forecast; Appendix A. Elementary probability theory; Appendix B. Stochastic processes; Appendix C. Elementary differential geometry; References; Index.

John Harlim is a Professor of Mathematics and Meteorology at the Pennsylvania State University. His research interests include data assimilation and stochastic computational methods. In 2012, he received the Frontiers in Computational Physics award from the Journal of Computational Physics for his research contributions on computational methods for modeling Earth systems. He has previously co-authored another book, Filtering Complex Turbulent Systems (Cambridge, 2012).

'The MATLAB code used for the examples in the book can be downloaded from the publisher's website; the scripts are short, well commented and can be understood without difficulty (even if you are not a MATLAB expert).' Fabio Mainardi, MAA Reviews

• 1. Introduction; 2. Markov chain Monte Carlo; 3. Ensemble Kalman filters; 4. Stochastic spectral methods; 5. Karhunen–Loève expansion; 6. Diffusion forecast; Appendix A. Elementary probability theory; Appendix B. Stochastic processes; Appendix C. Elementary differential geometry; References; Index.

John Harlim is a Professor of Mathematics and Meteorology at the Pennsylvania State University. His research interests include data assimilation and stochastic computational methods. In 2012, he received the Frontiers in Computational Physics award from the Journal of Computational Physics for his research contributions on computational methods for modeling Earth systems. He has previously co-authored another book, Filtering Complex Turbulent Systems (Cambridge, 2012).

'The MATLAB code used for the examples in the book can be downloaded from the publisher's website; the scripts are short, well commented and can be understood without difficulty (even if you are not a MATLAB expert).' Fabio Mainardi, MAA Reviews

• 1. Introduction; 2. Markov chain Monte Carlo; 3. Ensemble Kalman filters; 4. Stochastic spectral methods; 5. Karhunen–Loève expansion; 6. Diffusion forecast; Appendix A. Elementary probability theory; Appendix B. Stochastic processes; Appendix C. Elementary differential geometry; References; Index.